# A P Singh Complex Analysis Book pdf DOWNLOAD [Infostudy books PDF]

Complex analysis by ap singh pdf is helpful for CSIR-NET, IITAM, GATE, TIFR, NBHM and other such exam with similar syllabus.

This book is designed for the students who are preparing for various National Level competitive examinations and also inspires to enter into Ph.D. Programs by qualifying the various entrance exams.

This book starts with basic fundamental definitions of complex numbers and then the concepts of elementary functions, complex integration, power series, convergence and uniform convergence, singularities, residues, contour integration, conformal mappings, bilinear transformations etc. are discussed. The concepts of limit, continuity and differentiablity of complex functions are also explained in detail with good examples. This book aims at helping students to get into an insight view of the complex functions of complex variables and will alsoenable them to solve the problems by an easy and effective approach.

The practice sets are introduced at the end of the topics which includes a variety of questions from CSIR UGC NET, IIT JAM, TIFR, NBHM and GATE previous year question papers. These questions are carefully selected so that the students can apply mathematical knowledge in solving the questions. In addition to it, the solved examples are also given at the end of every chapter which will help in deep understanding of the topics discussed. The key points provides the quick revision of every chapter. Also, a well-thought question bank, in the form of various assignments is given at the end of each chapter which covers entire prescribed topics, so as to facilitate students to do more and more practiceand hence secure good results.

While compiling this book, more stress is given on problem solving technique rather than language or exact mathematical symbols.

## Overview of A P Singh Complex Analysis Book AUTHOR :

Dr A.P. Singh is Ph.D. In mathematics from Panjab university. He has been a Gold Medalist in his graduation as well as post-commencement and a recipient of countrywide Board of better arithmetic (NBHM) scholarship besides being a sportsman and a chess lover. He cleared his CSIR UGC JRF in December 2000 at the same time as he become pursuing his Masters diploma. All through his Ph.D., he has been conferred with the accolades like Indian young Scientist Award, Prof M. Venkataraman best Paper Presentation Award.  After finishing studies, he earned name and repute for his sustained efforts in offering satisfactory schooling to his students lots of whom are actually pursuing studies in IITS, IISERs, Panjab college, Delhi university and different reputed establishments. For the final 15 years, Dr A.P. Singh is committed to promoting better arithmetic by using his precise way of teaching,  guiding and motivating students to crack the country wide stage checks like net, GATE, TIFR, IIT-JAM, and many others., so that they may pursue their career in higher mathematics.

Dr A.P. Singh is constantly inclined to take up college students’ issues on fb organization “better Maths discussion through Dr A.P. Singh”.

## A P Singh Complex Analysis Book CONTENTS

CHAPTER – 0 : BASIC CONCEPTS OF COMPLEX NUMBERS.

• 0.1. DEFINITION OF COMPLEX NUMBER
• 0.2. ALGEBRA OF COMPLEX NUMBERS.
• 0.3. COMPLEX PLANE
• 0.4. CONJUGATE OF A COMPLEX NUMBER.
• 0.5. MODULUS OF A COMPLEX NUMBER.
• 0.6. ARGUMENT OR AMPLITUDE OF A COMPLEX NUMBER.
• 0.7. SOME REPRESENTATIONS OF A COMPLEX NUMBER..
• 0.8. USE OF COMPLEX NUMBERS IN CO-ORDINATE GEOMETRY…
• 0.9. DE MOIVRE’S THEOREM
• 0.10. SERIES EXPANSION OF SOME TRIGONOMETRIC FUNCTIONS.
• 0.11. ROOTS OF A COMPLEX NUMBER
• 0.12. EULER’S FORMULA
• 0.13. SPHERICAL REPRESENTATION OF COMPLEX NUMBERS (STEREOGRAPHIC PROJECTION)
• 0.14. CHORDAL DISTANCE
• KEY POINTS..
• ASSIGNMENT – 0.1
• ASSIGNMENT – 0.2.
• ASSIGNMENT – 0.3

CHAPTER – 1 : ELEMENTARY FUNCTIONS

• 1.1. SOME BASIC DEFINITIONS.
• 1.2. ELEMENTARY FUNCTIONS
• KEY POINTS
• ASSIGNMENT – 1.1.
• ASSIGNMENT – 1.2
• ASSIGNMENT – 1.3
• CHAPTER – 2 : ANALYTICITY & C-R EQUATIONS
• 2.1. CONTINUITY..
• 2.2. UNIFORM CONTINUITY
• 2.3. DERIVATIVES.
• 2.4. L’HOSPITAL RULE …
• 2.5. ANALYTIC FUNCTION.
• 2.6. CAUCHY-RIEMANN EQUATIONS
• 2.7. HARMONIC FUNCTIONS
• 2.8. CONSTRUCTION OF ANALYTIC FUNCTION.
• KEY POINTS
• ASSIGNMENT – 2.1
• ASSIGNMENT – 2.2.
• ASSIGNMENT – 2.3.

CHAPTER – 3 : COMPLEX INTEGRATION

• 3.1. SOME DEFINITIONS
• 3.2. LINE INTEGRAL
• 3.3. COMPLEX LINE INTEGRAL
• 3.4. CAUCHY’S THEOREM
• 3.5. CAUCHY’S INTEGRAL FORMULAE
• 3.6. SOME IMPORTANT THEOREMS
• KEY POINT.
• ASSIGNMENT – 3.1
• ASSIGNMENT – 3.2
• ASSIGNMENT – 3.3

CHAPTER – 4 : SEQUENCE AND SERIES

• 4.1. SEQUENCE
• 4.2. INFINITE SERIES
• 4.3 POWER SERIES.
• 4.4. TAYLOR’S SERIES.
• 4.5. LAURENT’S SERIES..
• KEY POINTS.
• ASSIGNMENT 4.1.
• ASSIGNMENT 4.2.
• ASSIGNMENT 4.3.

CHAPTER 5 : CLASSIFICATION OF SINGULARITIES AND LAURENT SERIES

• 5.1. ZEROS AND SINGULAR POINTS
• 5.2. ENTIRE FUNCTION
• 5.3. MEROMORPHIC FUNCTION
• 5.4. RESIDUE.
• 5.5. THE RESIDUE THEOREM
• 5.6. CHARACTERIZATION OF RATIONAL FUNCTIONS
• 5.7. CHARACTERIZATION OF POLYNOMIALS
• 5.8. THE ARGUMENT THEOREM..
• 5.9. IMPORTANT THEOREMS.
• KEY POINTS.
• ASSIGNMENT 5.1.
• ASSIGNMENT 5.2.
• ASSIGNMENT 5.3.

CHAPTER 6 : EVALUATION OF DEFINITE INTEGRALS
AND BILINEAR TRANSFORMATIONS .

• 6.1. CONTOUR INTEGRATION
• 6.2. CONFORMAL MAPPING.
• 6.3. INVERSE POINTS…..
• 6.4. BILINEAR TRANSFORMATION.
• KEY POINTS
• ASSIGNMENT – 6.1
• ASSIGNMENT – 6.2
• ASSIGNMENT – 6.3
• INDEX …

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